Linear equation word problem

Question

To receive an A in a course, Steve must obtain an average score of 90 or higher on 5 exams. If Stevens first four exam scores are 92, 87, 96 and 77 what is the minimum score that Steve can receive on the fifth exam to get an A in the course?

Answer 1

Let x = Steve's grade on the fifth exam.

 

Steve gets an A if:

   (92+87+96+77+x)/5 ≥ 90

   (352+x)/5 ≥ 90         [collect terms]

    (352+x) ≥ 450         [multiply both sides by +5 retains sense of inequality]

        x ≥ 98                 [subtract +352 from both sides retains sense of inequality]

 

Steve must score a 98 or higher to get a A in the course.

 

Note:  Here is an alternative method:

92 + 87 + 96 + 77 + x ≥ 5*90

92 + 87 + 96 + 77 + x ≥ 90 + 90 + 90 + 90 + 90

(92-90) + (87-90) + (96-90) + (77-90) + (x-90) ≥ 0         [group scores with desired average]

    2       -   3        +    6        -  13         +  (x-90) ≥ 0      [calculate points gained/lost on each test]

               -8                                         + x -90 ≥ 0

                                                              x ≥ 98        [add 98 to both sides retains inequality]

Answer 2

Hi Brittany.

Let's call the score on Steve's fifth exam x.  We know that the average of x plus the scores on the first four exams must be greater than 90.  So we express the average of all five exams equalling the minimum score of 90 to get an A as follows:

(92 + 87 + 96 + 77 + x)/5 = 90

Now solve for x:

(352 + x)/5 = 90

Multiply both sides by 5 and subtract 352 from both sides to determine x:

x = 90*5 - 352 = 98

So Steve must get a 98 or higher on the last test in order to have an average score on all five tests of 90 or higher.

 

Check: (92 + 87 + 96 + 77 + 98)/5 =90

 

Note: I'll bet he wishes he'd done better than a 77 on the fourth test!)